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A limit theorem for a class of stationary increments L\'{e}vy moving average process with multiple singularities
- Source :
- Ljungdahl, M M & Podolskij, M 2018, ' A limit theorem for a class of stationary increments Levy moving average process with multiple singularities ', Modern Stochastics: Theory and Applications, vol. 5, no. 3, pp. 297–316 . https://doi.org/10.15559/18-VMSTA111, Modern Stochastics: Theory and Applications, Vol 5, Iss 3, Pp 297-316 (2018)
- Publication Year :
- 2018
-
Abstract
- In this paper we present some new limit theorems for power variations of stationary increment L\'{e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528, Festschrift for Bernt {\O}ksendal, Stochastics 81(1) (2017), 360--383] under the assumption that the kernel function potentially exhibits a singular behaviour at $0$. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653--677] that studied the same mathematical question for the class of Brownian semi-stationary models.<br />Comment: Published at https://doi.org/10.15559/18-VMSTA111 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)
- Subjects :
- Statistics and Probability
Class (set theory)
Moving averages
fractional processes
01 natural sciences
Lévy process
010104 statistics & probability
High frequency data
Moving average
Limit (mathematics)
Stable convergence
0101 mathematics
Mathematics
Levy processes
lcsh:T57-57.97
lcsh:Mathematics
010102 general mathematics
Mathematical analysis
limit theorems
lcsh:QA1-939
Moving-average model
Lévy processes
Modeling and Simulation
lcsh:Applied mathematics. Quantitative methods
moving averages
Gravitational singularity
Statistics, Probability and Uncertainty
stable convergence
Mathematics - Probability
high frequency data
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ljungdahl, M M & Podolskij, M 2018, ' A limit theorem for a class of stationary increments Levy moving average process with multiple singularities ', Modern Stochastics: Theory and Applications, vol. 5, no. 3, pp. 297–316 . https://doi.org/10.15559/18-VMSTA111, Modern Stochastics: Theory and Applications, Vol 5, Iss 3, Pp 297-316 (2018)
- Accession number :
- edsair.doi.dedup.....5d305638fe585e15709f2b39a15509fa